Introduction to Mathematical Logic

Author: Elliot Mendelsohn

Publisher: Springer Science & Business Media

ISBN: 1461572886

Category: Science

Page: 342

View: 6116

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This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
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Automated Reasoning with Analytic Tableaux and Related Methods

International Conference, TABLEAUX 2000 St Andrews, Scotland, UK, July 3-7, 2000 Proceedings

Author: Roy Dyckhoff

Publisher: Springer

ISBN: 3540450084

Category: Computers

Page: 440

View: 8878

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This book constitutes the refereed proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2000, held in St Andrews, Scotland, UK, in July 2000.The 23 revised full papers and 2 system descriptions presented were carefully reviewed and selected from 42 submissions. Also included are 3 invited lectures and 6 nonclassical system comparisons. All current issues surrounding the mechanization of reasoning with tableaux and similar methods are addressed - ranging from theoretical foundations to implementation, systems development, and applications, as well as covering a broad variety of logical calculi.
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Proof Complexity and Feasible Arithmetics

DIMACS Workshop, April 21-24, 1996

Author: Paul W. Beame,Samuel R. Buss

Publisher: American Mathematical Soc.

ISBN: 9780821870822

Category: Mathematics

Page: 320

View: 4961

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Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether or not logical inferences can be made but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether or not NP is equal to co-NP. In addition, these have important implications for the efficiency of automated reasoning systems. The last dozen years have seen several breakthroughs in the study of these resource requirement. Papers in this volume represent the proceedings of the DIMACS workshop on "Feasible Arithmetics and Proof Complexity" held in April 1996 in Rutgers, NJ, as part of the DIMACS Institute's Special Year on Logic and Algorithms. This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.
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AI*IA 99:Advances in Artificial Intelligence

6th Congress of the Italian Association for Artificial Intelligence Bologna, Italy, September 14-17, 1999 Selected Papers

Author: Associazione italiana per l'intelligenza artificiale. Congress,Italian Association for Artificial Intelligence. Congress (,Congress of Italian Association for Artificial Intelligence (,Associazione Italiana per l'Intelligenza Artificiale

Publisher: Springer Science & Business Media

ISBN: 3540673504

Category: Computers

Page: 392

View: 1289

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This book constitutes the thoroughly refereed post-conference proceedings of the 6th Congress of the Italian Association for Artificial Intelligence, AI*IA 99, held in Bologna, Italy, in September 1999. The 33 revised full papers presented were carefully reviewed and selected for inclusion in the book from a total of 64 congress submissions. The papers are organized in topical sections on knowledge representation; automated reasoning; temporal and qualitative reasoning; machine learning, data mining, and theory revision; natural language processing and web interfaces; multi-agent systems; perception and robotics; and planning and scheduling.
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Books in series

1876 - 1949 ; original, reprinted, in-print, and out-of-print books, publ. or distributed in the US in popular, scholarly, and professional series

Author: [Anonymus AC00083573],[Anonymus AC00083576]

Publisher: N.A

ISBN: 9780835226790

Category:

Page: N.A

View: 3270

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AI*IA ...

Advances in Artificial Intelligence : ... Congress of the Italian Association for Artificial Intelligence ... Selected Papers

Author: Associazione italiana per l'intelligenza artificiale. Congress

Publisher: N.A

ISBN: N.A

Category: Artificial intelligence

Page: N.A

View: 7325

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